A triangle ABC is inscribed in a circle with center O. The line CD is perpendicular to the plane of the circle and of length CD=10cm. If angle DAC= , the angle DBC= and AB=6.67cm calculate the angle subtended by each of the sides of the triangle ABC at the center O.

I calculated AC=4.00cm and BC=5.70cm. I don't know what to do next. I've tried using the cosine rule to find in terms of r, the radius of the circle, the angles, then find the value of r from the area.

Area=

Area=

so then r=

Then i filled in r into and got, where

I solve this equation for but the values of were greater than 1 so this is the wrong approach.

Thanks